Hi
Have u shown it to any orthopaedic Dr? As u r saying when u do twisting movement it gets little better,it means stretching eases ur pain, so definitely u have got some tightness in ur back muscles. But u need an XRay at least to see the condition of spine and disc height to rule out any disc pathology.
Next Steps
Get an X Ray done
Health Tips
Hot pack would b a better option ,and while sleeping straight keep a pillow beneath it knees and between ur knees in case u r lying down on ur side.